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Mathochism: Over-thinking it

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

We had our second geometry test Thursday, and I wish I could say I did well. But I’m quite certain I didn’t. Yes, yes. I say that every time! But I know for a fact that I got the first, third and fourth problem wrong. And when a test only has eight questions in the first place, three wrong doesn’t lead to an A.

True, I didn’t have high expectations for this one. It covered a lot of material, since Uchitel was hell-bent on catching up. And even with a study guide, the process felt a lot like triage. Should I focus more on triangles? Or proportions? Or quadrilaterals? Or parallel lines? Why am I dreaming of being attacked by special triangles?
During the studying process, I wound up filling out a stack of flash cards as thick as the textbook. It was twice the size of my classmate’s stack in the next seat, and hers prompted Uchitel to ask if she had copied the whole book. In my case, that was probably true!

The monster stack, however, didn’t help me. If anything, it may have hindered me, because it gave me too many possibilities, it made me over-think. And it didn’t help that the very first problem befuddled me the most. (I was sitting in Befuddled Girl’s usual spot during the test. Coincidence? Curse?)

Anyway, the problem was about special triangles, and involved the following figure:

We had to find the length of certain sides, with side DC given as 6 square root of 3, and angle RCD as 30 degrees. The 30-degree-angle thing defined the problem as one involving special triangles. The formula for a 30-60-90 triangle is a, a square root of 3, 2a. Sounds simple, yes? Just plug and chug!

But this is where the over-thinking part came in. Since this was a rectangle, I assumed that the 90-degree angle in triangle DRC was angle DRC. Then I drove myself bats for way too long multiplying square roots before realizing that for anything to work, I had to assume the 90-degree angle was RDC. Which breaks all the rules of rectangles I had so painstakingly put down on my monster stack of flashcards! So I just wound up writing “Impossible!” on the problem, and moving on to the rest of the test.

Had I not been so preoccupied, I would have realized that I was struggling over the wrong triangle. To solve the problem, I needed to focus on triangle DAC, which was an obvious special triangle. This was always an option, but I simply couldn’t see the forest for the trees. Of course, the problem would have been easy had the figure looked like this:

But it didn’t.

As frustrating as this test experience was, I’m glad I was able to figure things out. I can’t guarantee I won’t over-think things again. But at least now I know I’m prone to it, and will do my best to fight it.

All text copyrighted by A.K. Whitney, and cannot be used without permission.

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2 comments

Over-thinking was always a problem, for me. I found that I’d get sucked into a problem, focus on one way to solve it, and not be able to think of it a different way.

What got me out of that (although, of course, this is just what worked for me and might not work for anyone else) was reading the whole test first, and jotting down comments on what to do for each problem. That usually took about five minutes. And then I’d go and work on the easiest problems, and if I got stuck I’d move to the next. By halfway through the test, I’d have some problems done, and ideas written down for each. And then I’d go back and tackle the hard problems.

I think that by switching from problem to problem, I minimized my over-focusing on one problem, and I could come back to a problem where I was stuck with a somewhat different gaze.